Exact Solutions with Symmetry Reduction and Long Time Behaviors of Non-linear Partial Differential Equations
A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".
Deadline for manuscript submissions: closed (30 September 2023) | Viewed by 10627
Special Issue Editors
Interests: partial differential equations; symmetry reduction; blowup; euler-poisson equations; euler equations with or without coriolis force; camassa-holm equations; navier-stokes equations; Magnetohydrodynamics (MHD); analytical and exact solutions; mathematical methods in fluids; classical cosmology
Special Issues, Collections and Topics in MDPI journals
Interests: analytic solutions of non-linear partial differential equations; laser-atom interaction
Interests: continuous and discrete integrable systems; nonlinear waves with applications; scientific computing and numerical analysis; nonlinear optics and optical fiber communications
Interests: nonlinear mathematical physics; applications of lie group to differential equations
Special Issue Information
Dear Colleagues,
It is well-known that most nonlinear partial differential equations do not have a general solution in closed form. However, by using symmetry reductions we can construct their special exact solutions, which can reflect the properties or long time behaviors of the nonlinear partial differential systems. In other words, symmetry is especially useful in the analysis of some particular cases of complex systems.
Similarly, it is often possible to write down some special exact solutions explicitly in terms of elementary functions, and those elementary functions often appear in a highly symmetric form.
In this Special Issue, we are expecting theoretical or numerical analyses of some special solutions with symmetry assumptions of some nonlinear partial differential systems, such as those arising in fluid mechanics (original or special cases of the Navier–Stokes equations, Euler equations, Euler–Poisson equations, etc.), general relativity (original or special cases of the Einstein field equations, etc.), and other nontrivial and nonlinear partial differential equations.
Submit your paper and select the Journal “Symmetry” and the Special Issue “Exact Solutions with Symmetry Reduction and Long Time Behaviors of Non-linear Partial Differential Equations” via: MDPI submission system. Our papers will be published on a rolling basis and we will be pleased to receive your submission once you have finished it.
Prof. Dr. Manwai Yuen
Dr. Imre Ferenc Barna
Prof. Dr. Baofeng Feng
Prof. Dr. Biao Li
Prof. Dr. Li Jun Zhang
Guest Editors
Manuscript Submission Information
Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.
Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.
Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.
Keywords
- nonlinear partial differential equations
- symmetry reduction
- exact solutions
- fluid dynamics
- solution in closed form
- qualitative properties
Benefits of Publishing in a Special Issue
- Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
- Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
- Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
- External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
- e-Book format: Special Issues with more than 10 articles can be published as dedicated e-books, ensuring wide and rapid dissemination.
Further information on MDPI's Special Issue polices can be found here.